Mana is an attribute that is used in determining your MP. That is to say, it's not the same thing as MP, (which is represented by the blue bar on the bottom of the screen,) although it does have a significant impact upon it.
Mana serves as a multiplier upon your total MP - a character with 200 Mana will have twice as many MP as a character with 100 Mana. For the exact formula of how MP is determined, see the MP page.
Mana is based overwhelmingly upon your race, and is displayed under the middle column of the character screen. 100 Mana is the "standard" Mana score of humanoids, while Golems have the least Mana, at 70, while Liches have 140. This functionally allows different races to have different MP growth rates.
Mana can be increased, although not by a huge factor without going to extreme lengths. The Magical Gene series of feats will increase mana by 5 for every feat level, up to a maximum of 25. Eating a magic fruit increases mana by 3, and equipment made out of dawn cloth increases it by 5. Magic Fruit can theoretically be farmed through capturing extremely large numbers of little sisters.
Keep in mind that some abilities can instantly drain all MP and force a mana reaction that will harm the player based upon their total MP, so high Mana can potentially be a liability, especially if it far outpaces HP and/or Life unless you are willing to increase the Magic Capacity skill. (And even then, higher Mana makes training the skill more difficult.)